I'm glad you found a work around for at least one game.
However, like I said originally......this is a problem for the manufacturer to address even if Apple caused the problem. It is up to the manufacturer to ensure their product works properly with any support hardware, plus they are the only ones who can possibly get Apple's attention to address a macOS if it is indeed an unexpected bug from some macOS update. Sometimes when an OS patches a security issue, it can have negative consequences on existing apps & hardware.....that usually means the third party manufacturer or developer needs to modify their product accordingly....sometimes that may not always be easy depending on what changed (fortunately such extreme cases are rare).
Plus games (on a computer) are a completely different beast than other regular apps and always have been for decades.
I don't know anything about this controller (never heard of it before)....does the manufacturer even claim it is compatible with those games you are using? Many times a game may only officially support certain controllers. Other controllers are probably trying to pretend to be an officially supported controller, but may well fall short of it. Plus most third party developers & manufacturers focus primarily on Windows compatibility and only slightly support other platforms....which is very unfortunate.
Does the controller have any software updates or firmware updates that may address the issues you are encountering?
Try checking the Steam forums and the games' forums to see if anyone else is encountering this problem. I would even check to see if Windows users are having similar issues...if so, then you probably have no hope of proper support for macOS.
I wish you luck in getting this controller working with your games.